Such a depilating apparatus is known, for example, from Japanese utility model 57-54725. The depilating member and the clamping member in this model are constructed as rollers which are rotatable about parallel axes. The contact surface between the two rollers is only small so that a tensile force is exerted only for a short period of time on a hair which is clamped between the rollers. A cover plate is present to prevent the skin from getting in the comparatively large wedge-shaped entrance space between the rollers and from being also clamped between the rollers. Short hairs having a length in the order of the thickness of the cover plate cannot be clamped by the rollers as a result of the cover plate.